Investigation of positive definite solution of nonlinear matrix equation Xp=Q+∑i=1mAi∗XδAi

In this paper, we consider the nonlinear matrix equation X p = Q + ∑ i = 1 m A i ∗ X δ A i , where A i ( i = 1 , 2 , … , m ) are n × n nonsingular complex matrices, Q is a n × n Hermitian positive definite (HPD) matrix, p ≥ 1 , m ≥ 1 are positive integers, and δ ∈ ( 0 , 1 ) . We discuss the solution...

Full description

Saved in:
Bibliographic Details
Published in:Computational & applied mathematics 2021, Vol.40 (3)
Main Authors: Jin, Zhixiang, Zhai, Chengbo
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied physics
Banach spaces
Computational mathematics
Computational Mathematics and Numerical Analysis
Fixed points (mathematics)
Mathematical analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Matrix methods
Perturbation methods
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we consider the nonlinear matrix equation X p = Q + ∑ i = 1 m A i ∗ X δ A i , where A i ( i = 1 , 2 , … , m ) are n × n nonsingular complex matrices, Q is a n × n Hermitian positive definite (HPD) matrix, p ≥ 1 , m ≥ 1 are positive integers, and δ ∈ ( 0 , 1 ) . We discuss the solution of this equation via properties of Thompson metric and two fixed point theorems in ordered Banach spaces and estimate the bounds of the HPD solution. Furthermore, perturbation analysis is investigated.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-021-01463-0